Using the laplace transformation table, evaluate the following, considering any other variable other than t as constant unless otherwise stated: b. If x = t – 4, find L[(xe^−x)]

Q: Let f(x) = Bx2 + 6 t where Bis a constant. If the slope of the tangent line to the graph of f at æ =…

A: f(x)=Bx2+6sqrt(x).

Q: Evaluate the following integrals. (a) (b) Sx√4 x√4 + x² dx

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Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

A: A detailed solution is given below.

Q: 3 f(x) = x³ + 2 right left [-1,1] n = 2 9=1 & middle hand rule b =

A: find out the left, right and mid riemann sum.

Q: What is the lim 0 (sing - )? If your answer is a Whole Number Fraction (+) Positive Infinity (-)…

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Q: What is the lim_0+ 2²-In(x) For answers write... that are in decimal form and round off to fractions…

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Q: 7 For what value of k are the vectors u Select one alternative: Ok=-1 Ok=-2 Ok=1 Ok=2 (1,-1,-1) and…

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Q: How do you evaluate this integral using trigonometric substitution?

A: Here x2 -a2  type we use trigonometry substitution by x=a sec(θ)

Q: Given: f(x, y) = 3xey - 2ye-x Find: 0² f(x,y) Әх у 0 3x - 2e"* 0 Зе" + 2e-* 0 3e 0 3x + 2e-*

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Q: m³ The volume of a large spherical balloon is increasing at a rate of 64 balloon's surface area…

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Q: Use a table of integrals to evaluate the following indefinite integral. The integrals may require…

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Q: For the following exercises, draw the region bounded by the curves. Then, find the volume when the…

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Q: y=xe

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: What is the slope of the tangent line to the curve y = at the point (3,)?

A: What is the slope of the tangent line to the curve y=1x at a point 3, 13 ?

Q: A balloon which maintains the shape of a sphere is being inflated. The rate of change of its volume…

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Q: Evaluate the line integral F(x, y, z) = (x,-z, y). Jo F. dr where C is given by r(t) = (2t, 3t,…

A: We will use concept of parameterization to solve this.

Q: 4.2.3. Find the integrating factor by inspection then solve the following differential equation.…

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Q: 32 Which one of the following is the general antiderivative G(a), for g(x) Note: CER Select one…

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral…

A: Solve the following

Q: Given a vector function (a) Find the domain of r(t). (b) Find the limit lim r(t). t→1 (c) Find the…

A: The objective is to solve the above question.

Q: Identify and sketch the graph of y = r²+1 in R³.

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Q: For which values of a and b E R is the following piecewise function continuous on IR? sin(a )+ ax0 x…

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Q: Given the differential equation y'' − 3y' – 4y = - 2 sin(2t), y(0) = 0, y'(0) = - = - 1 Apply the…

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Q: 17 For what value of k will the following system of equations have an infinite number of solutions?…

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Q: e2x (x²-4) Given: y = Determine the following: a. Symmetry b. Intercepts c. Vertical Asymptote/s d.…

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Q: If c is a constant, what is the limit of c as x approaches a? 0 C a X

A: A detailed solution is given below.

Q: Find and sketch the domain of the function. f(x, y) - In(4x2 - 4y²) y

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Q: Evaluate the integral. The integral from 0 to t of 9sin^2(x) dx  Then determine whether the…

A: A detailed solution is given below.

Q: wing is Of has a relative minima at x = -3 and x = 3. OIt cannot be determined if has any relative…

A: To find the relative maximum and minimum of the function

Q: What is f 5√xdx? 3 f 5√√xdx = 5x² + C 2 3 f5√xdx = 10x² + C 3 f5√xdx = 5x² + C 3 [ 5vxdx= 5x? +C

A: Let's solve given integral.

Q: Find the area of the region bounded above by y = x2 + 8 and below by y = 4. 10- 4 2 X -10 8 6 4/-2…

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Q: 0 Given the piecewise function f(x) = 5-x 5-z What is f (4) ? Answer: f4 (4) = What is f¹ (4) ?…

A: Given function:-

Q: Find the volume of the given solid. Under the plane 3x + 2y - z = 0 and above the region enclosed by…

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Q: 6. DETAILS ZILLDIFFEQMODAP11 1.2.009. MY NOTES ASK YOUR TEACHER In this problem, x = C₁ cost + c₂…

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Q: Find the first partial derivatives of the function. f(x, y) = x6y3 + 4x7y

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Q: A particle moves back and forth along a straight line. Its position (in meters), relative to the…

A: Find out the total distance travelled during the first 10 seconds.

Q: The number of bacteria in a refrigerated food product is given by N(T) = 23T² – 96T + 12, 5 < T < 35…

A: The number of bacteria in a refrigerated food product is given by N(T) = 23T2-96T+12,  5&lt;T&lt;35…

Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. Find the unit vector…

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Q: Which one of the following is the gradient of the tangent line at the point (5, 1) on the graph of,…

A: To find the gradient of the tangent line of the point (5,1) on the graph of x+xy+2y2=12 Formulae…

Q: Given: f(x, y, z) = e¯ª sin(yz) Find: ² f(x, y, z) əyəx O z cos(yz) et O cos(yz) e O-ze-* cos(yz) O…

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Q: Determine whether the series Σn=1 3n+¹ ln(n+1) is convergent or divergent.

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Q: Find the volume of the solid formed by revolving the graph of y = 2e- on the interval [0, ∞) about…

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Q: dx What is , where dy' x³ + y³ = 3xyusing differentiation? implicit dx dy y-x² y² +x dx y-x y²-x dy…

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Q: Find the first partial derivatives of the function. f(r, s) = r ln(r³ +56) fr(r, s) = fs(r, s) =

A: To find out the first partial derivatives.

Q: find the higher partial derivative of the following

A: Solve the following

Q: Suppose two positive real numbers a and b add to 120. Find the values of a and b that maximize the…

A: Given a+b=120 .....1

Q: Graph the parabola. y=x+2x-2 Plot five points on the parabola: the vertex, two points to the left of…

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Q: Assume a and y are functions of a third variable t. If xy = 30 and 10, find dt 0-6 0-3/1/20 O-12…

A: Here we use the concept of derivatives

Q: Determine a root of f(x) = 2* +3 cos(x²)-2 with 10-3 accuracy.

A: Given :f(x)=2x+3cosx2-2

Q: Given the piecewise function f(x) = Why is f not differentiable at x = 5? Of is continuous at x = :5…

A: This question is based on continuity of function.